Solution for a Semi-Permeable Interface Crack Between Two Dissimilar Piezoelectric Material

2006 ◽  
Vol 74 (5) ◽  
pp. 833-844 ◽  
Author(s):  
Q. Li ◽  
Y. H. Chen
Keyword(s):  
Interface Crack ◽  
Hilbert Problem ◽  
Piezoelectric Materials ◽  
Electric Displacement ◽  
Crack Tip ◽  
Crack Model ◽  
Permeable Crack ◽  
Variable Theory ◽  
Impermeable Crack ◽  
Silicon Oil

A semi-permeable interface crack in dissimilar piezoelectric materials is studied in detail. Attention is focused on the influence induced from the permittivity of the medium inside the crack gap on the near-tip singularity and the crack tip energy release rate (ERR). The Stroh complex variable theory (Stroh, A. N., 1958, Philos. Mag. 3, pp. 625–646;Ting, T. C. T., Int. J. Solids Struct., 22, pp. 965–983) is used to obtain the solution, from which some useful numerical results for 21 kinds of dissimilar piezoelectric materials are calculated. They are combined from seven kinds of commercial piezoelectric ceramics. The distribution of the normal electric displacement component (NEDC) along the interface crack is assumed to be uniform and the corresponding problem is then deduced to a Hilbert problem with an unknown NEDC. Solving the Hilbert problem and determining the near-tip field for each of the 21 bimaterials, we determine the crack tip singularities and find that the crack-tip singularity for a certain combination of two dissimilar piezoelectric materials can be either oscillatory or nonoscillatory when the poling axes of both piezoelectric materials are perpendicular to the interface crack. Energy analyses for PZT‐4∕BaTiO3 as a typical nonoscillatory class bimaterial and those for PZT-5H∕BaTiO3 as a typical oscillatory class bimaterial are specially studied in detail under four different conditions: (i) the crack gap is filled with air or vacuum; (ii) the crack gap is filled with silicon oil to avoid discharge; (iii) the crack gap is conducting; and (iv) the electrically impermeable crack. Detailed comparisons are performed among the four cases. We conclude that the different values of the permittivity have no influence on the crack tip singularity but have significant influences on the crack tip ERR under the combined electromechanical loading. We also conclude that the previous investigations under the insulating crack model are incorrect or misleading since the model overestimates the effect of the electric field on the ERR very much and the results of the ERR for the impermeable crack show significant discrepancies from those for the semi-permeable crack. Whereas the previous investigations under the conducting crack model may be accepted in a tolerant, way, the results of the ERR show very small discrepancies from those for the semi-permeable crack model, especially when it filled with silicon oil.

Solution for a Semi-Permeable Interface Crack in Elastic Dielectric/Piezoelectric Bimaterials

2008 ◽  
Vol 75 (1) ◽  
Author(s):  
Q. Li ◽  
Y. H. Chen
Keyword(s):  
Electric Field ◽  
Mechanical Loading ◽  
Interface Crack ◽  
Applied Electric Field ◽  
Crack Tip ◽  
Crack Model ◽  
Permeable Crack ◽  
Impermeable Crack ◽  
Silicon Oil ◽  
Elastic Dielectric

A semi-permeable interface crack in infinite elastic dielectric/piezoelectric bimaterials under combined electric and mechanical loading is studied by using the Stroh complex variable theory. Attention is focused on the influence induced from the permittivity of the medium inside the crack gap on the near-tip singularity and on the energy release rate (ERR). Thirty five kinds of such bimaterials are considered, which are constructed by five kinds of elastic dielectrics and seven kinds of piezoelectrics, respectively. Numerical results for the interface crack tip singularities are calculated. We demonstrate that, whatever the dielectric phase is much softer or much harder than the piezoelectric phase, the structure of the singular field near the semi-permeable interface crack tip in such bimaterials always consists of the singularity r−1∕2 and a pair of oscillatory singularities r−1∕2±iε. Calculated values of the oscillatory index ε for the 35 kinds of bimaterials are presented in tables, which are always within the range between 0.046 and 0.088. Energy analyses for five kinds of such bimaterials constructed by PZT-4 and the five kinds of elastic dielectrics are studied in more detail under four different cases: (i) the crack is electrically conducting, (ii) the crack gap is filled with air/vacuum, (iii) the crack gap is filled with silicon oil, and (iv) the crack is electrically impermeable. Detailed comparisons on the variable tendencies of the crack tip ERR against the applied electric field are given under some practical electromechanical loading levels. We conclude that the different values of the permittivity have no influence on the crack tip singularity but have significant influences on the crack tip ERR. We also conclude that the previous investigations under the impermeable crack model are incorrect since the results of the ERR for the impermeable crack show significant discrepancies from those for the semi-permeable crack, whereas the previous investigations under the conducting crack model may be accepted in a tolerant way since the results of the ERR show very small discrepancies from those for the semi-permeable crack, especially when the crack gap is filled with silicon oil. In all cases under consideration the curves of the ERR for silicon oil are more likely tending to those for the conducting crack rather than to those for air or vacuum. Finally, we conclude that the variable tendencies of the ERR against the applied electric field have an interesting load-dependent feature when the applied mechanical loading increases. This feature is due to the nonlinear relation between the normal electric displacement component and the applied electromechanical loadings from a quadratic equation.

The Higher Order Crack Tip Fields for Interfacial Crack between Linear Functionally Graded and Homogeneous Piezoelectric Materials

2014 ◽  
Vol 1015 ◽  
pp. 97-100
Author(s):  
Yao Dai ◽  
Xiao Chong ◽  
Ying Chen
Keyword(s):  
Piezoelectric Materials ◽  
Electric Displacement ◽  
Interfacial Crack ◽  
Crack Tip ◽  
Higher Order ◽  
Functionally Graded ◽  
Linear Functions ◽  
Intensity Factors ◽  
Crack Tip Fields ◽  
Functionally Graded Piezoelectric Materials

The higher order crack-tip fields for an anti-plane crack situated in the interface between functionally graded piezoelectric materials (FGPMs) and homogeneous piezoelectric materials (HPMs) are presented. The mechanical and electrical properties of the FGPMs are assumed to be linear functions of y perpendicular to the crack. The crack surfaces are supposed to be insulated electrically. By using the method of eigen-expansion, the higher order stress and electric displacement crack tip fields for FGPMs and HPMs are obtained. The analytic expressions of the stress intensity factors and the electric displacement intensity factors are derived.

The Interface Crack Between Dissimilar Anisotropic Composite Materials

1983 ◽  
Vol 50 (1) ◽  
pp. 169-178 ◽  
Author(s):  
S. S. Wang ◽  
I. Choi
Keyword(s):  
Composite Materials ◽  
Interface Crack ◽  
Hilbert Problem ◽  
Stress Singularity ◽  
Anisotropic Elasticity ◽  
Crack Model ◽  
Closed Crack ◽  
Anisotropic Composite ◽  
Interlaminar Crack ◽  
As Stress

The fundamental nature of an interface crack between dissimilar, strongly anisotropic composite materials under general loading is studied. Based on Lekhnitskii’s stress potentials and anisotropic elasticity theory, the formulation leads to a pair of coupled governing partial differential equations. The case of an interlaminar crack with fully opened surfaces is considered first. The problem is reduced to a Hilbert problem which can be solved in a closed form. Oscillatory stress singularities are observed in the asymptotic solution. To correct this unsatisfactory feature, a partially closed crack model is introduced. Formulation of the problem results in a singular integral equation which is solved numerically. The refined model exhibits an inverse square-root stress singularity for commonly used advanced fiber-reinforced composites such as a graphite-epoxy system. Extremely small contact regions are found for the partially closed interlaminar crack in a tensile field and, therefore, a simplified model is proposed for this situation. Physically meaningful fracture mechanics parameters such as stress intensity factors and energy release rates are defined. Numerical examples for a crack between θ and −θ graphite-epoxy composites are examined and detailed results are given.

Impermeable Crack and Permeable Crack Assumptions, Which One is More Realistic?

2004 ◽  
Vol 71 (4) ◽  
pp. 575-578 ◽  
Author(s):  
Bao-Lin Wang ◽  
Yiu-Wing Mai
Keyword(s):  
Boundary Condition ◽  
Piezoelectric Materials ◽  
Finite Width ◽  
Permeable Crack ◽  
Impermeable Crack ◽  
Electrical Boundary Conditions ◽  
Engineering Problems ◽  
Electrical Boundary Condition ◽  
Crack Faces ◽  
Impermeable Boundary

This paper investigates the applicability and effect of the crack-free electrical boundary conditions in piezoelectric fracture. By treating flaws in a medium as notches with a finite width, the results from different electrical boundary condition assumptions on the crack faces are compared. It is found that the electrically impermeable boundary is a reasonable one for engineering problems. Unless the flaw interior is filled with conductive media, the permeable crack assumption may not be directly applied to the fracture of piezoelectric materials in engineering applications.

On Global Energy Release Rate of a Permeable Crack in a Piezoelectric Ceramic

2003 ◽  
Vol 70 (2) ◽  
pp. 246-252 ◽  
Author(s):  
S. Li
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Crack Growth ◽  
Release Rate ◽  
Piezoelectric Ceramic ◽  
Piezoelectric Materials ◽  
Dielectric Medium ◽  
Crack Model ◽  
Permeable Crack ◽  
Global Energy

A permeable crack model is proposed to analyze crack growth in a piezoelectric ceramic. In this model, a permeable crack is modeled as a vanishing thin, finite dimension, rectangular slit with dielectric medium inside. A first-order approximation solution is derived in terms of the slit height, h0. The main contribution of this paper is that the newly proposed permeable crack model reveals that there exists a realistic leaky mode for electrical field, which allows applied electric field passing through the dielectric medium inside a crack. By taking into account the leaky mode effect, a correct estimation of electrical and mechanical fields in front of a crack tip in a piezoelectric ceramic is obtained. To demonstrate this new finding, a closed-form solution is obtained for a mode III permeable crack under both mechanical as well electrical loads. Both local and global energy release rates are calculated based on the permeable crack solution obtained. It is found that the global energy release rate derived for a permeable crack is in a broad agreement with some known experimental observations. It may be served as a fracture criterion for piezoelectric materials. This contribution reconciles the outstanding discrepancy between experimental observation and theoretical analysis on crack growth problem in piezoelectric materials.

A Crack in an Electrode Layer between Two Dissimilar Piezoelectric Materials

2007 ◽  
Vol 353-358 ◽  
pp. 231-234
Author(s):  
Hyeon Gyu Beom ◽  
Y.H. Kim ◽  
C.K. Yoon ◽  
Chong Du Cho
Keyword(s):  
Closed Form ◽  
Interface Crack ◽  
Analytic Functions ◽  
Piezoelectric Materials ◽  
Interfacial Crack ◽  
Crack Tip ◽  
Crack Tip Field ◽  
Electrode Layer ◽  
Finite Crack ◽  
Electromechanical Loading

A crack on the conductive interface between two dissimilar piezoelectric ceramics under electromechanical loading is investigated. The closed form of the singular crack tip fields for the interface crack is derived here using an analysis based on analytic functions. It is shown that the interfacial crack-tip field consists of a pair of oscillatory singularities. A closed form of the solution for a finite crack on the conductive interface between dissimilar piezoelectric media is also derived.

The Higher Order Mechanical and Electric Fields for Arbitrarily Oriented Crack with the Physical Weak-Discontinuity

2014 ◽  
Vol 602-605 ◽  
pp. 283-286
Author(s):  
Yao Dai ◽  
Xiao Chong
Keyword(s):  
Electric Fields ◽  
Piezoelectric Materials ◽  
Electric Displacement ◽  
Crack Tip ◽  
Expansion Method ◽  
Higher Order ◽  
Functionally Graded ◽  
Linear Functions ◽  
Intensity Factors ◽  
Functionally Graded Piezoelectric Materials

The higher order crack-tip fields for anti-plane crack oblique to the interface between functionally graded piezoelectric materials (FGPMs) and homogeneous piezoelectric materials (HPMs) are presented. The crack is oriented in arbitrary direction. The crack surfaces are assumed to be electrically impermeable. The material properties of FGPMs are assumed to be linear functions with their gradient direction perpendicular to the interface. By using the eigen-expansion method, the high order crack tip stress and electric displacement fields are obtained. The analytic expressions of the stress intensity factors and the electric displacement intensity factors are derived.

scholarly journals Anti – plane crack emanating from the interface in a bounded smart PEMO- elastic structure

2013 ◽  
Vol 18 (4) ◽  
pp. 1165-1199 ◽  
Author(s):  
B. Rogowski
Keyword(s):  
Magnetic Fields ◽  
Interface Crack ◽  
Integral Transform ◽  
Mixed Boundary ◽  
Electric Displacement ◽  
Closed Form Solution ◽  
Crack Tip ◽  
Shear Loading ◽  
Cauchy Kernel ◽  
Electric And Magnetic Fields

Abstract The magnetoelectroelastic analysis of two bonded dissimilar piezo-electro-magneto-elastic ceramics with a crack perpendicular to and terminating at the interface is made. By using the Fourier integral transform (in perpendicular directions in each materials), the mixed boundary conditions and continuity conditions are transformed to a singular integral equation with generalized Cauchy kernel, the solution of which has been well studied, and classical methods are directly applicable here to obtain the closed form solution. The results are presented for a permeable crack under anti-plane shear loading and in-plane electric and magnetic loadings, as prescribed electric displacement and magnetic inductions or electric and magnetic fields. The results indicate that the magnetoelectroelastic field near the crack tip in the homogeneous PEMO- elastic ceramic is dominated by a traditional inverse square-root singularity, while the coupled field near the crack tip at the interface exhibits the singularity of the power law r--α , r being the distance from the interface crack tip and α depending on the material constants of a bimaterial. In particular, electric and magnetic fields have no singularity at the crack tip in a homogeneous solid, whereas they are singular around the interface crack tip. Numerical results are given graphically to show the effects of the material properties on the singularity order, field intensity factors and energy release rates. The results presented in this paper should have potential applications to the design of multilayered magnetoelectroelastic structures.

Investigation of the critical states of dielectric cracks in functionally graded piezoelectric materials

2009 ◽  
Vol 465 (2110) ◽  
pp. 3187-3207
Author(s):  
Zhi Yan ◽  
Liying Jiang
Keyword(s):  
Crack Length ◽  
Critical State ◽  
Fourier Transforms ◽  
Piezoelectric Materials ◽  
Functionally Graded ◽  
Crack Model ◽  
Permeable Crack ◽  
Critical States ◽  
Functionally Graded Piezoelectric Materials ◽  
Functionally Graded Piezoelectric

A critical state for electromechanical loads that determines when the traditional impermeable (or permeable) crack model serves as the upper or the lower bound of the dielectric crack model, first proposed for homogeneous piezoelectric materials, is studied further for functionally graded piezoelectric materials (FGPMs) in the current work. The analytical formulations of a single crack and two interacting cracks in the FGPMs are derived by using Fourier transforms, and the resulting integral equations are solved with Chebyshev polynomials. Numerical simulations are conducted to show the effect of crack length, positions of two interacting cracks and material gradient of FGPMs at this critical state. Interesting results show that the combination of the material gradient and the crack length α a plays an important role in determining this critical state. Our solutions also reveal there may exist several critical states for two interacting cracks in the FGPMs.

The Crack Tip Fields for Anti-Plane Interfacial Crack between Functionally Graded and Homogeneous Piezoelectric Materials

2014 ◽  
Vol 989-994 ◽  
pp. 719-722
Author(s):  
Yao Dai ◽  
Xiao Chong
Keyword(s):  
Intensity Factor ◽  
Piezoelectric Materials ◽  
Electric Displacement ◽  
Interfacial Crack ◽  
Crack Tip ◽  
Expansion Method ◽  
Functionally Graded ◽  
Displacement Fields ◽  
Functionally Graded Piezoelectric Materials ◽  
Electric Displacement Intensity Factor

The problem of an anti-plane crack situated in the interface of functionally graded piezoelectric materials (FGPMs) and homogeneous piezoelectric materials (HPMs) is considered under the impermeable assumption of crack surfaces. The mechanical and electrical properties of the FGPMs are assumed to be exponential functions of y perpendicular to the crack. The higher order crack tip stress and electric displacement fields for FGPMs and HPMs are obtained by the eigen-expansion method. The stress intensity factor and electric displacement intensity factor are obtained explicitly.

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